Cook the penne pasta according to package instructions until al dente. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the diced chicken and season with salt and pepper. Cook until the chicken is browned and cooked through, about 5-7 minutes.
Add the minced garlic to the skillet and sauté for 1 minute until fragrant.
Stir in the broccoli florets and cook for another 3-4 minutes until the broccoli is tender but still bright green.
Reduce the heat to low and pour in the heavy cream. Stir to combine, then add the Parmesan cheese and Italian seasoning. Mix until the cheese is melted and the sauce is creamy.
Add the cooked penne to the skillet and toss until the pasta is well coated with the sauce. Adjust seasoning with salt and pepper if needed.
Serve hot, garnished with fresh parsley.